In the early 1980s, Harvey M. Schwartz was working weekends in the cold room of a kosher butcher shop in New Jersey, shaping beef into hamburger patties.

Two hundred miles away in upstate New York, David M. Solomon was a frat brother playing rugby and mulling an entry-level banking position.

More than three decades later, the two men are competing for what may be the most coveted job on Wall Street: running Goldman Sachs.

Longtime managers of separate arms of the company, Mr. Schwartz, 53, and Mr. Solomon, 55, were named co-chief operating officers and presidents of Goldman last December when Gary Cohn, who previously held the titles, joined the Trump administration. The dual promotions made the men overnight adversaries in the race to run Goldman — that is, whenever Lloyd C. Blankfein, its longstanding chairman and chief executive, steps aside.

The 63-year-old Mr. Blankfein once joked that he planned to die at his desk. But at 11 years, his tenure exceeds those of his recent predecessors, and guessing his replacement has become a popular Wall Street parlor game.

Mr. Schwartz, a black belt in karate, spends many Sunday afternoons in the office. Over five hours of interviews for this article, the most revealing moment about his business psychology came when he described how he interviews job candidates: He asks them to try to sell him the Polycom speakerphone that sits on his desk.

Aside from a brief stint in the mid-2000s, the two co-presidents have not previously worked together. Now, they’re immersed in an indefinite on-the-job competition against each other — and they are unlikely to know who won until shortly before Mr. Blankfein’s departure is made public. The board’s succession planning is ongoing, but the details of it are closely guarded, said a person familiar with the process who was not authorized to speak publicly.

Image

Mr. Schwartz records a podcast at Goldman Sachs.CreditGoldman Sachs

Current and former Goldman executives say Mr. Blankfein appears unlikely to step aside for at least a year, and he may end up staying for several more. Mr. Blankfein declined to comment.

The race to run Goldman comes at a rare moment of vulnerability for the bank.

Goldman is still highly profitable. So far this year, it has churned out $8 billion in pretax profit. Its stock price values the company at $90 billion. Making partner there remains a yearned-for rank on Wall Street.

But new regulations are clipping profits. Public scrutiny is intense, increasing the likelihood and costs of embarrassing gaffes. Perhaps most important, Goldman’s trading unit, long the engine of its profits, has struggled to adapt to the post-crisis world. In 2009, that business peaked at $33 billion in revenue. This year, the company is on track to make about a third of that.

Mr. Schwartz and Mr. Solomon need to come up with ways to compensate for that slide. In April, they presented their proposals to the board: increase lending and financing activities, expand bond trading and do more banking in cities like Atlanta and Seattle. They calculated that those steps, plus a few others, would generate $5 billion in additional revenue over three years.

The outcome of those efforts is likely to influence who gets picked to lead their firm’s next generation.

From the Gym to the Executive Suite

Mr. Schwartz was born in Morristown, N.J. His father was a scientist. His mother died of cancer when he was 14. Feeling rudderless after high school, he began working as a trainer at a gym. A Rutgers University alumna pressed him to apply to her alma mater — and marched him to campus for an interview after he was turned down initially. He got in on the second try.

“Rutgers was the first place I started to develop my own sense of confidence,” Mr. Schwartz said on a recent walk around the Piscataway campus where he lived for four years, majoring in economics.

The six-foot, four-inch Mr. Schwartz held an assortment of odd jobs in college. He was a nightclub bouncer. He ran a quick-service landscaping outfit. He worked at the butcher shop. He learned to expertly sharpen knives.

“If I come over to your house at Thanksgiving and I sharpen your knife, you will definitively know the difference right away,” he joked during an interview in his 41st-floor office.

After college, Mr. Schwartz got into finance. His first day on a trading floor was Oct. 19, 1987. The stock market plunged 22 percent on what came to be known as Black Monday. He remembers a colleague crying.

“If you’re around that environment, I don’t know anybody that couldn’t be sensitized to the cyclical nature of the markets,” Mr. Schwartz said. It left him with a permanent sense of jitters over how easily capital can be destroyed.

A decade later, he was hired at J. Aron, the Goldman commodities unit. One of his first tasks was to establish operations in Australia, where gold miners were eager for ways to protect themselves from market swings by setting up financial hedges. He created elaborate presentation booklets for clients and — anxious that they might get misplaced — lugged massive boxes of them onto the plane from New York.

“He’s always been a good shepherd internally in terms of managing risk and balancing that with clients’ interests,” said Kevin Ulrich, who knew Mr. Schwartz as a Goldman colleague before leaving in 2003 to run the hedge fund Anchorage Capital.

In 2001, Mr. Blankfein — then running Goldman’s bonds-trading division — promoted Mr. Schwartz to be co-head of the unit’s sales team. At the meeting to announce the elevation, Mr. Schwartz was sitting in the audience when he overheard a woman use some blue language to ask her neighbor who on earth he was. He tapped on the back of her chair and whispered, “Hi, I’m Harvey.”

By 2013, Mr. Schwartz had ascended to the job of Goldman’s chief financial officer, making him one Mr. Blankfein’s top lieutenants and the bank’s face in the investment community.

Mr. Schwartz is cautious and can be tightly scripted. As a general rule, he waits 48 hours to collect his thoughts before addressing someone who has really annoyed him. Some colleagues say he has a tendency to “mark to market” his underlings — meaning that, in accounting terms, he assesses their value to his objectives and treats them accordingly. That has frustrated some people.

Image

David Solomon performing as D.J. D-Sol, one of his pastimes.CreditGotophotography, via The EM Awards

Betting on Goldman

Mr. Solomon had a more traditional résumé for Goldman’s C-suite. He grew up in suburban Hartsdale, N.Y. and spent summers as a camp counselor in New Hampshire. He attended a liberal arts school and joined a fraternity. After graduating, he joined the commercial bank Irving Trust.

In the early 1990s, Mr. Solomon joined Bear Stearns, where he helped run the bank’s junk bonds division, working with bankers and salespeople to devise and sell higher-risk bonds. At one point, he helped a Dallas movie theater company, which was struggling to finance its expansion into Mexico, raise money through a complicated bond transaction.

Mr. Solomon also built a varied social network, holding an annual holiday party at his Upper West Side home that mixed people from Wall Street with neighbors his wife knew from walking the dog in Central Park.

In 1997, Mr. Solomon worked alongside Jon Winkelried, then the co-head of Goldman’s bond division, on a deal to raise money for the Venetian resort in Las Vegas. Mr. Winkelried was impressed with Mr. Solomon’s handling of the deal and offered him a job running Goldman’s leveraged finance team, again raising capital for companies through higher-risk bonds. It was a rare instance of Goldman hiring an outsider and awarding him the rank of partner.

Mr. Solomon, 37 at the time, surprised colleagues by defecting from Bear.

“I thought he was on the leadership track at Bear,” said Phil Berney, who worked with him there. “But he saw it” — Goldman — “as a great, long-dated franchise to get involved with.”

“It was a step back,” acknowledged Mr. Solomon during a recent interview in his office, four doors down from Mr. Schwartz’s. “ I was running a division of a firm and I went and I took a job running a department.” But Bear’s leaders at the time were reluctant to expand globally, and Mr. Solomon worried that without a broader reach, Bear could be left behind. Goldman, he felt, was on firmer footing.

For a short time in the mid-2000s, Mr. Solomon was Mr. Schwartz’s boss in a group within Goldman’s investment bank. But Mr. Schwartz soon was promoted to help run another division. After that, they kept largely to separate orbits.

Starting in 2006, Mr. Solomon was co-head of Goldman’s investment bank, a job he held for the next decade. Once, he showed up to pitch for the Lululemon Athletica initial public offering wearing a maroon jacket and long sweatpants made by the brand. His colleagues were similarly outfitted. “Everyone on the other side of the table is in suits and ties,” Mr. Solomon recalled. “It threw people off.” Goldman won a lead role on Lululemon’s I.P.O.

Image

Mr. Solomon takes a selfie at a Goldman office in India.CreditGoldman Sachs

An Uneasy Alliance

On Jan. 18 this year, in one of his last acts as finance chief, Mr. Schwartz announced Goldman’s annual results. Among his duties that day was to brief hundreds of Goldman managing directors, in an auditorium at the company’s headquarters. He delivered a smooth, confident presentation, graciously thanking “the federation” — Goldman’s term for its accounting, financial and other back-office employees — for its hard work.

Then things got awkward. Mr. Blankfein — who was participating by phone from the World Economic Forum in Davos, Switzerland — invited Mr. Solomon to say a few words. But Mr. Solomon was also in Switzerland and had been told ahead of time he would not have to speak. Taken aback, he remarked briefly on his client meetings in the Alps, and then returned the floor to Mr. Blankfein.

Some employees speculated that Mr. Blankfein was trying to give equal airtime to the two presidents. Others wondered whether perhaps he had deliberately caught Mr. Solomon off guard.

The incident, slight as it was, was talked about for weeks afterward. It was a sign of the intensifying internal gossip about what some referred to as the “Hunger Games”-style jockeying for the top job.

The two men are now striving to showcase their skills — whether it comes to wooing clients or setting priorities inside the bank.

On Feb. 5, Rob Roy, the chief executive of a data center operator called Switch, said he was attending the Super Bowl with his family when his cellphone rang. It was Mr. Solomon, who was sitting nearby with clients and had heard Mr. Roy was also at the game. He wanted Switch to pick Goldman for the company’s planned initial public stock offering. Mr. Roy and Mr. Solomon, who had not previously met, decided to have a quick introduction in the stadium concourse, Mr. Roy recalled, that turned into a half-hour conversation. Goldman last month won the lucrative role as the lead investment bank on Switch’s I.P.O.

Mr. Solomon also leaned on executives in Goldman’s human resources office to hire far more women. Given the nearly even split in society, he argued, there was no reason that Goldman’s ranks should not be equally balanced between men and women. He has taken that message on the road, too.

The shy Mr. Schwartz has adapted less easily to the spotlight. He spent hours preparing for his first television appearance in June on CNBC, where the first question was about Goldman’s “Game of Thrones.” He took multiple stabs at recording his recent podcast.

He, too, is chasing clients. On a trip to China in May, Mr. Schwartz asked an official from the China Investment Corporation, the government’s sovereign-wealth fund, how Goldman could deepen its relationship there. The resultant conversation, in which the two men discussed the symbolic importance of joint investing, set the stage for a $5 billion investment partnership between Goldman and C.I.C. that was announced Nov. 9.

As the presidents crisscross the world, they are never far from each other’s minds — or inboxes. On a recent trip to Riyadh, Saudi Arabia, Mr. Schwartz said he had been in frequent touch with Mr. Solomon through voice mail and email. He was heading back to New York the next day.

“And when I land tomorrow … when I go to the office, I only have a handful of meetings tomorrow,” he said. “And David is one of them.”

Correction:

An earlier version of this article misstated the surname of the chief executive of Switch. As correctly noted elsewhere in the article, he is Rob Roy, not Rob Rob.

A version of this article appears in print on , on Page BU1 of the New York edition with the headline: 2-Man Race To Be No. 1 At Goldman. Order Reprints | Today’s Paper | Subscribe